Determine the intercepts of the line. $ y-3=5(x-2)$ $y$ -intercept: $\Big($
Solution: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y-3&=5({0}-2)\\ y-3&=-10\\ y&=-7\end{aligned}$ So the $y$ -intercept is $\left(0,-7\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}-3&=5(x-2)\\ -3&=5x-10\\ 7&=5x\\ 1.4&=x\end{aligned}$ So the $x$ -intercept is $\left(1.4,0\right)$. In conclusion, The $y$ -intercept is $\left(0,-7\right)$. The $x$ -intercept is $\left(1.4,0\right)$.